Efficient encoding/decoding apparatus

ABSTRACT

An efficient encoding/decoding apparatus of this invention comprises orthogonal transform element (10) for orthogonally transforming a digital signal obtained by allowing an analog signal to undergo analog/digital conversion, quantizer (11) for quantizing the digital signal which has undergone orthogonal transform processing, inverse quantizer (21) for inverse-quantizing a digital signal which is not yet caused to undergo inverse orthogonal transform processing, and inverse orthogonal transform element (20) for inverse-orthogonally transforming the orthogonally transformed digital signal, wherein rounding in even number direction or rounding in odd number direction is used in at least one of the orthogonal transform processing and the inverse orthogonal transform processing. Thus, accumulation of rounding errors at the time of, e.g., such a direct digital dubbing to repeatedly encode/decode digital signals such as video signals, etc. is prevented, thus making it possible to reduce picture deterioration of multi-generation characteristic.

TECHNICAL FIELD

This invention relates to an efficient encoding/decoding apparatus, andmore particularly to such an efficient encoding/decoding apparatuscapable of suppressing accumulation (storage) of errors in repeatedlyencoding/decoding digital signals, e.g., video signals, etc.

BACKGROUND ART

In recent years, as an efficient encoding/decoding apparatus adapted forcompression-encoding a digital signal thereafter to decode such encodedsignal, there have appeared such digital VTRs adapted tocompression-encode, e.g., a digital video signal to record such encodedsignal onto a recording medium to decode a signal reproduced from therecording medium.

In the above-mentioned VTRs, a procedure as described below is generallyemployed to compress a video signal to record the compressed signal tofurther reproduce the recorded signal to expand it.

Namely, although not shown, digital video data on the time axisdelivered to signal recording system (encoding side) is first caused toundergo orthogonal transform processing, e.g., Discrete Cosine Transform(DCT), etc. so that such data is transformed into data on the frequencyaxis. The video data on the frequency axis is quantized and is furthercaused to undergo, e.g., variable length encoding, etc. so that suchdata is compressed. The compressed video data is recorded onto amagnetic tape as a recording medium.

Moreover, at signal reproducing system (decoding side), the compressedvideo data recorded on the recording medium is reproduced. Thisreproduced data is expanded by variable length decoding, and is furthercaused to undergo inverse quantization. The inversely quantized data iscaused to undergo Inverse Discrete Cosine Transform (IDCT) as inverseorthogonal transform so that the video data on the frequency axis isrestored into video data on the time axis for a second time. Thereafter,such restored video data will be taken out.

As digital VTR for carrying out compression-encoding of such videosignal, there are, e.g., digital VTRs using, e.g., predictive encodingsystem between frames/between fields. In such digital VTR, it isnecessary to allow local decode picture for carrying out the predictiveencoding at the encoding side and decode picture of the decoding side tobe in correspondence with each other. At this time, there is the problemthat if operation methods at inverse transform (inverse orthogonaltransform) in local decoding at the encoding side and inverse transform(inverse orthogonal transform) at the decoding side and rounding methodsat the encoding side and the decoding side are different, miss matchwhich will be described later may take place. For this reason, in therecommendation H.261 (Television conference/telephone low speed movingpicture encoding algorithm) in Comite Consultatif InternationaleTelegraphique et Telephonique (CCITT), quantization representativevalues are caused to be odd number as shown in Table 1.

                                      TABLE 1                                     __________________________________________________________________________    QUANTIZATION REPRESENTATIVE VALUE OF QUANTIZATION WITH DEAD ZONE              QUANT     1   2   3   4   .                                                                              8   9   .                                                                              17  18  .                                                                              30  31                           \                                                                   QUANTIZATION                                                                  INDEX                                                                         __________________________________________________________________________    -127      -255                                                                              -509                                                                              -765                                                                              -1019                                                                             .                                                                              -2039                                                                             -2048                                                                             .                                                                              -2048                                                                             -2048                                                                             .                                                                              -2048                                                                             -2048                        -126      -253                                                                              -505                                                                              -759                                                                              -1011                                                                             .                                                                              -2023                                                                             -2048                                                                             .                                                                              -2048                                                                             -2048                                                                             .                                                                              -2048                                                                             -2048                        .         .   .   .   .   .                                                                              .   .   .                                                                              .   .   .                                                                              .   .                            -2        -5  -9  -15 -19 .                                                                              -39 -45 .                                                                              -85 -89 .                                                                              -149                                                                              -155                         -1        -3  -5  -9  -11 .                                                                              -23 -27 .                                                                              -51 -53 .                                                                              -89 -93                          0         0   0   0   0   .                                                                              0   0   .                                                                              0   0   .                                                                              0   0                            1         3   5   9   11  .                                                                              23  27  .                                                                              51  53  .                                                                              89  93                           2         5   9   15  19  .                                                                              39  45  .                                                                              85  89  .                                                                              149 155                          3         7   13  21  27  .                                                                              55  63  .                                                                              119 125 .                                                                              209 217                          4         9   17  27  35  .                                                                              71  81  .                                                                              153 161 .                                                                              269 279                          5         11  21  33  43  .                                                                              87  99  .                                                                              187 197 .                                                                              329 341                          .         .   .   .   .   .                                                                              .   .   .                                                                              .   .   .                                                                              .   .                            56        113 225 339 451 .                                                                              903 1017                                                                              .                                                                              1921                                                                              2033                                                                              .                                                                              2047                                                                              2047                         57        115 229 345 459 .                                                                              919 1035                                                                              .                                                                              1955                                                                              2047                                                                              .                                                                              2047                                                                              2047                         58        117 233 351 467 .                                                                              935 1053                                                                              .                                                                              1989                                                                              2047                                                                              .                                                                              2047                                                                              2047                         59        119 237 357 475 .                                                                              951 1071                                                                              .                                                                              2023                                                                              2047                                                                              .                                                                              2047                                                                              2047                         60        121 241 363 483 .                                                                              967 1089                                                                              .                                                                              2047                                                                              2047                                                                              .                                                                              2047                                                                              2047                         .         .   .   .   .   .                                                                              .   .   .                                                                              .   .   .                                                                              .   .                            125       251 501 753 1003                                                                              .                                                                              2007                                                                              2047                                                                              .                                                                              2047                                                                              2047                                                                              .                                                                              2047                                                                              2047                         126       253 505 759 1011                                                                              .                                                                              2023                                                                              2047                                                                              .                                                                              2047                                                                              2047                                                                              .                                                                              2047                                                                              2047                         127       255 509 765 1019                                                                              .                                                                              2039                                                                              2047                                                                              .                                                                              2047                                                                              2047                                                                              .                                                                              2047                                                                              2047                         __________________________________________________________________________

Namely, as shown in the Table 1 mentioned above, in the above-mentionedrecommendation H.261, quantization representative values are odd numberexcept for -2048. Employment of odd number as the quantizationrepresentative value is to solve the problem that even if the IDCTstandard is satisfied, miss match may take place between IDCT ofdifferent designs. In the Table 1, quantization representative valuesare symmetrical in positive and negative directions except for+2047/-2048. In addition, step size is equal to 2×QUANT.

Meanwhile, while the above-mentioned miss match is caused by the factthat operation methods and/or rounding methods in inverse transformprocessing are different, even in the case where operation methodsand/or rounding methods in the inverse transform processing are notdifferent, similar problem may take place.

For example, in digital VTRs, the problem of picture degradation(deterioration) in multi-generation characteristic at the time of directdigital dubbing may take place as the above-mentioned miss match.

Namely, there is the problem that pattern emphasis by monotonousincrease or decrease of amplitude level of a certain specific picturepattern takes place.

The reason why picture degradation takes place in the multi-generationcharacteristic at the time of direct digital dubbing in the digital VTRwill now be described with reference to the attached drawings.

The configuration employed in the case where the above-mentioned directdigital dubbing is carried out in the digital VTR is shown in FIG. 1.

In this FIG. 1, an input video signal delivered through terminal 103 isrecorded on magnetic tape in digital VTR 100. Output terminal of thedigital VTR 100 and input terminal of digital VTR 101 are connected, andoutput terminal of digital VTR 101 and input terminal of digital VTR100are connected. In respective digital VTRs 100, 101,recording/reproduction is repeated, whereby multi-dubbing is carriedout. In this example, output terminal of digital VTR 106 is connectedalso to monitor 102. Accordingly, it is possible to observe change ofpicture quality by multi-dubbing by means of the monitor 102.

Moreover, the respective digital VTRs 100, 101 of FIG. 1 are digital VTRof component recording in which bit rate reduction is employed. It isnow assumed that, as the system of bit rate reduction, transformencoding+variable length encoding is employed and the DCT mentionedabove is employed as transform basic (basis) function. Further, it isassumed that these respective digital VTRs 100, 101 are adapted tosupport system of 10 bit video, and operation accuracy oftransform-inverse transform (DCT-IDCT) is thus adjusted under thecondition where operation word length is taken (ensured) so as tosufficiently satisfy such video accuracy.

Simplified configuration for carrying out direct digital dubbing shownin FIG. 1 can be as shown in FIG. 2.

Namely, in FIG. 2, terminal 103 is supplied with data from one digitalVTR as input data, and this input data is caused to undergo DCT by DCTCircuit 111. Coefficient data from the DCT circuit 111 is quantized byre-quantizer (quantization/inverse quantization element) 112, and itsoutput is sent to IDCT circuit 113. Rounding error Erc takes place inoutput from the re-quantizer 112. Moreover, rounding error Ers takesplace also in output from the IDCT circuit 113 and output of the IDCTcircuit 113 is sent to the DCT circuit 111. in this example, rounding ininfinity direction which will be described later is employed for thisrounding. Output of IDCT circuit 113 is sent to monitor, etc. fromterminal 104.

Moreover, when multi-dubbing in FIG. 2 is expressed by further differentrepresentation, such multi-dubbing can be indicated as shown in FIG. 3.In FIG. 3, the case where, e.g., two times of dubbing operations (i.e.,the case where three times of transform-inverse transform operations arecarried out) is shown. The two times of dubbing operations correspond tothe fact that three sets of configurations each comprised of DCT circuit111, quantizer/inverse quantizer 112, and IDCT circuit 113 are connectedin series.

When the relationship between word length of input/output and thesignificant digit is expressed in a conceptual manner in theconfiguration of FIG. 2, such relationship can be expressed as shown inFIG. 4.

In FIG. 4, coefficients (AC coefficients) except for DC coefficient areuniformly quantized. Here, quantization step of DC coefficient isassumed to be qdc and quantization step of AC coefficient is assumed tobe qac. Moreover, normalized DCT, IDCT are used. At this time, therelationship between bits of coefficient plane and re-quantization stepis expressed below:

    qxx=divisor

    quantization level=qxx.Q[coefficient/qxx]

In the above expression, Q[ ] indicates rounding.

Accordingly, for example,

qdc=qac=1 . . . rounding into coefficient plane 12 bits

qdc=qac=2 . . . rounding into coefficient plane 11 bits

qdc=qac=4 . . . rounding into coefficient plane 10 bits

In digital VTR as described above, when it is assumed that there is noproblem because sufficient accuracy is ensured in operation of DCT-IDCT,it is considered that generation of picture degradation (monotonousincrease or decrease of specific picture pattern) at the time of directdigital dubbing results from the fact that rounding errors areaccumulated.

Here, as the rounding system, there are, e.g., simple rounding (roundingin positive direction) or rounding in infinity direction, etc.Differences between these rounding systems will now be described below.

Rounding in positive direction (simple rounding) will be first describedwith reference to FIG. 5.

In FIG. 5, mark  in the figure indicates that value marked in this wayis not included and mark  indicates that value marked in this way isincluded. Namely, in A and B of FIG. 5, when value is more than -Δ/2 andis less than Δ/2, value within that range is rounded into 0; when valueis more than Δ/2 and is less than 3Δ/2, value within that range isrounded into 1·2^(-b) ; when value is more than 3Δ/2 and is less than5Δ/2, value within that range is rounded into 2·2^(-b) ; when value ismore than -3Δ/2 and is less than -Δ/2, value within that range isrounded into -1·2^(-b) ; and when value is more than -5Δ/2 and is lessthan -8Δ/2, value within that range is rounded into -2·2^(-b). Inaddition P( ) of C indicates probability.

In the rounding in positive direction (simple rounding), since judgmentis carried out only by bits to carry out rounding, boundary point isalways rounded up. Accordingly, as designated at C of FIG. 5, errorvalue always includes Δ/2. As a result, distribution of errors deviates.It should be noted that the boundary point is the just half of bitsubject to rounding, i.e., ±0.5, and is point where asymmetry appears inthe distribution of errors.

From facts as described above, rounding in infinity direction isconventionally used.

The rounding in infinity direction will now be described with referenceto FIG. 8.

Also in this FIG. 8, mark  in the figure indicates that value marked inthis way is not included and mark  indicates that value marked in thisway is included. Namely, in A and B of FIG. 6, when value is greaterthan -Δ/2 and is less than Δ/2, value within that range is rounded into0; when value is more than Δ/2 and is less than 3Δ/2, value within thatrange is rounded into 1·2^(-b) ; when value is more than 3Δ/2 and isless than 5Δ/2, value within that range is rounded into 2·2^(-b) ; whenvalue is more than -3Δ/2 and is less than -Δ/2, value within that rangeis rounded into -1·2^(-b) ; and when value is more than -5Δ/2 and isless than -3Δ/2, value within that range is rounded into -2·2^(-b). Inaddition, P( ) of C of FIG. 8 also indicates probability.

In this rounding in infinity direction, boundary point is rounded up sothat positive and negative values are the same in terms of absolutevalue. Accordingly, there result three kinds of distributions of errorsas indicated by (a)˜(c) of C of FIG. 6, and these distributions oferrors are balanced with X=0 being as center.

As stated above, in rounding, it is seen that only point of Δ/2 is pointwhich allows the range of error to be out of balance.

Explanation will now be given in more practical sense.

Here, data of pixels of 2×2 on the time axis is assumed to be expressedbelow:

    ______________________________________                                                    D00 D01                                                                       D10 D11,                                                          ______________________________________                                    

and data of pixels of 2×2 on the frequency axis is assumed to beexpressed below:

    ______________________________________                                                    C00 C01                                                                       C10 C11                                                           ______________________________________                                    

Moreover, in order to reduce portions subject to rounding operation, DCTof pixel data of 2×2 and IDCT of pixel data of 2×2 corresponding theretoare expressed as follows:

    ______________________________________                                        DCT                                                                           C00 = D00 + D01 + D10 + D11                                                   C01 = D00 - D01 + D10 - D11                                                   C10 = D00 + D01 - D10 - D11                                                   C11 = D00 - D01 - D10 + D11                                                   IDCT                                                                          D00 = (C00 + C01 + C10 + C11)/4                                               D01 = (C00 - C01 + C10 - C11)/4                                               D10 = (C00 + C01 - C10 - C11)/4                                               D11 = (C00 - C01 - C10 + C11)/4                                               ______________________________________                                    

Here, change of data in the case where two times of dubbing operations,i.e., three times of encoding/decoding processing are implemented is asfollows. As the rounding method at this time, rounding in infinitydirection is used and step size of quantization is assumed to be 2.

Change of data in the case where, e.g., {3, 1, 1, 0} is given to inputis as follows.

    ______________________________________                                        Input              D = {3, 1, 1, 0}                                           First encoding/decoding                                                       After DCT          C = {5, 3, 3, 1}                                           After quantization/inverse                                                                       C = {6, 4, 4, 2}                                           quantization                                                                  After IDCT before rounding                                                                       D = {4.0, 1.0, 1.0, 0.0}                                   After IDCT after rounding                                                                        D = {4, 1, 1, 0}                                           Second encoding/decoding (First dubbing)                                      After DCT          C = {6, 4, 4, 2}                                           After quantization/inverse                                                                       C = {6, 4, 4, 2}                                           quantization                                                                  After IDCT before rounding                                                                       D = {4.0, 1.0, 1.0, 0.0}                                   After IDCT after rounding                                                                        D = {4, 1, 1, 0}                                           Third encoding/decoding (Second dubbing)                                      After DCT          C = {6, 4, 4, 2}                                           After quantization/inverse                                                                       C = {6, 4, 4, 2}                                           quantization                                                                  After IDCT before rounding                                                                       D = {4.0, 1.0, 1.0, 0.0}                                   After IDCT after rounding                                                                        D = {4, 1, 1, 0}                                           ______________________________________                                    

At the second operation and operations subsequent thereto, even ifencoding/decoding (i.e., dubbing) operations are implemented many times,there is no change in data.

Change of data in the case where, e.g., {1, 1, 1, 0} is given to inputis as follows:

    ______________________________________                                        Input              D = {1, 1, 1, 0}                                           First encoding/decoding                                                       After DCT          C = {3, 1, 1, -1}                                          After quantization/inverse                                                                       C = {4, 2, 2, -2}                                          quantization                                                                  After IDCT before rounding                                                                       D = {1.5, 1.5, 1.5, -0.5}                                  After IDCT after rounding                                                                        D = {2, 2, 2, -1}                                          Second encoding/decoding (First dubbing)                                      After DCT          C = {5, 3, 3, -3}                                          After quantization/inverse                                                                       C = {6, 4, 4, -4}                                          quantization                                                                  After IDCT before rounding                                                                       D = {2.5, 2.5, 2.5, -1.5}                                  After IDCT after rounding                                                                        D = {3, 3, 3, -2}                                          Third encoding/decoding (Second dubbing)                                      After DCT          C = {7, 5, 5, -5}                                          After quantization/inverse                                                                       C = {8, 6, 6, -6}                                          quantization                                                                  After IDCT before rounding                                                                       D = {3.5, 3.5, 3.5, -2.5}                                  After IDCT after rounding                                                                        D = {4, 4, 4, -3}                                          ______________________________________                                    

By implementation of the second encoding/decoding (i.e., dubbing)operations and operations subsequent thereto, data would change indivergence direction. In other words, rounding errors are accumulated.

As stated above, there are instances where when rounding in infinitydirection is used as a method of operation rounding in quantization andinverse quantization, data changes and diverges every time of dubbingwith respect to a certain input, i.e., rounding errors are accumulated.

In view of facts as described above, an object of this invention is toprovide an efficient encoding/decoding apparatus which permits picturedeterioration to be extremely less in multi-generation characteristic atthe time of, e.g., direct digital dubbing.

DISCLOSURE OF THE INVENTION

An efficient encoding/decoding apparatus according to this invention hasbeen proposed in order to attain the above-described object, andincludes orthogonal transform means for orthogonally transforming adigital signal obtained by allowing an analog signal to undergoanalog/digital conversion, and inverse orthogonal transform means forinverse-orthogonally transforming the orthogonally transformed digitalsignal, wherein rounding in even number direction or rounding in oddnumber direction is used in at least one of the orthogonal transformprocessing and the inverse orthogonal transform processing.

The efficient encoding/decoding apparatus of this invention is furtherprovided with quantizing means for quantizing the digital signal whichhas undergone the orthogonal transform processing, and inversequantizing means for inverse-quantizing a digital signal which is notyet caused to undergo the inverse orthogonal transform processing.

In accordance with this invention, rounding in even number direction orrounding in odd number direction is used in at least one of orthogonaltransform processing and inverse orthogonal transform processing tobalance the range of rounding error irrespective of polarity on spaceplane to prevent accumulation of rounding errors in multi-generationcharacteristic at the time of, e.g., direct digital dubbing, thuspermitting picture deterioration to be extremely less.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a view showing the configuration at the time of direct digitaldubbing of digital VTR.

FIG. 2 is a block circuit diagram showing, in simplified manner, theconfiguration of direct digital dubbing.

FIG. 3 is a block circuit diagram for explaining flow in the case ofcarrying out two times of dubbing operations.

FIG. 4 is a view showing, in a conceptual manner, the relationshipbetween input/output word length and significant digit of normalizedsimulation model in DCT-IDCT.

FIGS. 5A-5C are a view for explaining rounding in positive direction.

FIGS. 6A-6C are a view for explaining rounding in infinity direction.

FIG. 7 is a block circuit diagram showing outline of the configurationof an efficient encoding/decoding apparatus of an embodiment of thisinvention.

FIGS. 8A-8D are a view for explaining rounding in even number directionand odd number direction.

FIG. 9 is a view showing the range of error when quantization step sizeis set to 3.

FIG. 10 is a view showing simulation result of multi-dubbing when DCTand rounding in positive direction are used.

FIG. 11 is a view showing simulation result of multi-dubbing when DCTand rounding in infinity direction are used.

FIG. 12 is a view showing simulation result of multi-dubbing when DCTand rounding in even number direction are used.

FIG. 13 is a view showing simulation result of multi-dubbing when DCT atthe time of 12 bits of operation accuracy, rounding in even number,direction, rounding in infinity direction and rounding in positivedirection are used.

FIG. 14 is a view showing simulation result of multi-dubbing when DWTand rounding in positive direction are used.

FIG. 15 is a view showing simulation result of multi-dubbing when DWTand rounding in infinity direction are used.

FIG. 16 is a view showing simulation result of multi-dubbing when DWTand rounding in even number direction are used.

FIG. 17 is a view showing simulation result of multi-dubbing when DWT atthe time of operation accuracy 12 bits, rounding in even numberdirection, rounding in infinity direction and rounding in positivedirection are used.

FIG. 18 is a view showing group (1) of picture emphasis pattern.

FIG. 19 is a view showing group (2) of picture emphasis pattern.

FIG. 20 is a view showing group (3) of picture emphasis pattern.

FIG. 21 is a view showing group (4) of picture emphasis pattern.

BEST MODE FOR CARRYING OUT THE INVENTION

Preferred embodiment of this invention will now be described withreference to the attached drawings.

An efficient encoding/decoding apparatus of the embodiment of thisinvention includes, as shown in FIG. 7, orthogonal transform element 10for orthogonally transforming a digital signal obtained by allowing ananalog signal to undergo analog/digital conversion, and inverseorthogonal transform element 20 for inverse-orthogonally transformingthe orthogonally transformed digital signal, wherein rounding in evennumber direction or rounding in odd number direction is used in at leastone of the orthogonal transform processing and the inverse orthogonaltransform processing.

Moreover, the efficient encoding/decoding apparatus of this invention isfurther provided quantizer 11 for quantizing the digital signal whichhas undergone the orthogonal transform processing, and inverse quantizer21 for inverse-quantizing a digital signal which is not yet caused toundergo the inverse orthogonal transform processing.

In FIG. 7, a digital signal obtained by an allowing analog signal toundergo analog/digital conversion is delivered to terminal 1, and thisdigital signal is sent to orthogonal transform element 10 for carryingout, e.g., Discrete Cosine Transform (DCT) processing, etc. Digitalsignal orthogonally transformed from the time axis to the frequency axisat the orthogonal transform element 10 is quantized at quantizer 11, andis further compressed as the result of the fact that it is caused toundergo variable length encoding by variable length encoder 12. Thiscompressed digital data is recorded onto a recording medium by recordingmeans 13.

Moreover, the compressed digital data recorded on the recording mediumis reproduced by reproducing means 23. This reproduced data is expandedby variable length decoder 22, and is further caused to undergo inversequantization by inverse quantizer 21. The inverse-quantized data iscaused to undergo inverse orthogonal transform (e.g., Inverse DiscreteCosine Transform (IDCT)) by inverse orthogonal transform element 20 sothat the signal on the frequency axis is restored into digital signal onthe time base for a second time. Thereafter, the digital signal thusrestored is taken out from terminal 2.

While there are instances where the problem of picture deterioration maytake place as previously described in multi-generation characteristic atthe time of, e.g., direct digital dubbing in such digital VTR, thisinvention employs a scheme such that, in order to reduce such picturedeterioration, rounding in even number direction or rounding in oddnumber direction is used in at least one of the orthogonal transformprocessing, e.g., DCT and the inverse orthogonal transform processing,e.g., IDCT.

It should be noted that the above-mentioned rounding in even numberdirection carries out round-off or round-up so that rounded result ofthe boundary point necessarily becomes even number value.

Namely, in FIG. 8, mark  in the figure indicates that the value markedin such way is not included, and mark  indicates that the value markedin such way is included. In FIGS. 8A and 8B when value is more than -Δ/2and is less than Δ/2, value within that range is round into 0; whenvalue is more than Δ/2 and is less than 3Δ/2, value within that range isrounded into 1·2^(-b) ; when value is more than 3Δ/2 and is less than5Δ/2, value within that range is rounded into 2·2^(-b) ; when value ismore than -3Δ/2 and is less than -Δ/2, value within that range isrounded into -1·2^(-b) ; and when value is more than -5Δ/2 and is lessthan -3Δ/2, value within that range is rounded into -2·2^(-b). Inaddition, P() of FIG. 8C indicates probability.

In this rounding in even number direction, round-off or round-up iscarried out so that rounded result of boundary point necessarily becomeseven number value. Accordingly, there are two kinds of distributions oferrors as indicated by FIG. 8C and distribution of errors is "balancedwith respective numeric values being as center".

Explanation will now be given in more detail.

Here, similarly to the previously described prior art, data of pixels of2×2 on the time axis is expressed below:

    ______________________________________                                                    D00 D01                                                                       D10 D11                                                           ______________________________________                                    

and data of pixels of 2×2 on the frequency axis is expressed below:

    ______________________________________                                                    C00 C01                                                                       C10 C11.                                                          ______________________________________                                    

Moreover, DCT of pixel data of 2×2 and IDCT of 2×2 corresponding theretoare expressed as follows:

    ______________________________________                                        DCT                                                                           C00 = D00 + D01 + D10 + D11                                                   C01 = D00 - D01 + D10 - D11                                                   C10 = D00 + D01 - D10 - D11                                                   C11 = D00 - D01 - D10 + D11                                                   IDCT                                                                          D00 = (C00 + C01 + C10 + C11)/4                                               D01 = (C00 - C01 + C10 - C11)/4                                               D10 = (C00 + C01 - C10 - C11)/4                                               D11 = (C00 - C01 - C10 + C11)/4                                               ______________________________________                                    

Here, for quantization step size, as value except for power of 2, e.g.,3 is used, and two times of dubbing operations, i.e., three times ofencoding/decoding processing are implemented to input. Change of data inthis case is as follows.

Explanation will now be given in connection with the case where, e.g.,{1, 1, 1, 0} in which rounding errors are accumulated in rounding ininfinity direction of the previously described prior art is given toinput.

    ______________________________________                                        Input            D = {1, 1, 1, 0}                                             First encoding/decoding                                                       After DCT        C = {3, 1, 1, -1}                                            After quantization/inverse                                                                     C = {3, 0, 0, 0}                                             quantization                                                                  After IDCT before rounding                                                                     D = {0.75, 0.75, 0.75, 0.75}                                 After IDCT after rounding                                                                      D = {1, 1, 1, 1}                                             Second encoding/decoding (first dubbing)                                      After DCT        C = {4, 0, 0, 0}                                             After quantization/inverse                                                                     C = {3, 0, 0, 0}                                             quantization                                                                  After IDCT before rounding                                                                     D = {0.75, 0.75, 0.75, 0.75}                                 After IDCT after rounding                                                                      D = {1, 1, 1, 1}                                             Third encoding/decoding (second dubbing)                                      After DCT        C = {4, 0, 0, 0}                                             After quantization/inverse                                                                     C = {3, 0, 0, 0}                                             quantization                                                                  After IDCT before rounding                                                                     D = {0.75, 0.75, 0.75, 0.75}                                 After IDCT after rounding                                                                      D = {1, 1, 1, 1}                                             ______________________________________                                    

In a manner as stated above, even if continuous connections are mademany times at the second operation and operations subsequent thereto,data does not change.

Moreover, as the example using rounding in even number direction asrounding, explanation will now be given in connection with the examplewhere rounding in even number direction is used for, e.g., roundingafter IDCT.

    ______________________________________                                        Input              D = {1, 1, 1, 0}                                           First encoding/decoding                                                       After DCT          C = {3, 1, 1, -1}                                          After quantization/inverse                                                                       C = {4, 2, 2, -2}                                          quantization                                                                  After IDCT before rounding                                                                       D = {1.5, 1.5, 1.5, 0.5}                                   After IDCT after rounding                                                                        D = {2, 2, 2, 0}                                           Second encoding/decoding (first dubbing)                                      After DCT          C = {6, 2, 2, -2}                                          After quantization/inverse                                                                       C = {6, 2, 2, -2}                                          quantization                                                                  After IDCT before rounding                                                                       D = {2.0, 2.0, 2.0, 0.0}                                   After IDCT after rounding                                                                        D = {2, 2, 2, 0}                                           Third encoding/decoding (second dubbing)                                      After DCT          C = {6, 2, 2, -2}                                          After quantization/inverse                                                                       C = {6, 2, 2, -2}                                          quantization                                                                  After IDCT before rounding                                                                       D = {2.0, 2.0, 2.0, 0.0}                                   After IDCT after rounding                                                                        D = {2, 2, 2, 0}                                           ______________________________________                                    

In a manner as stated above, even if continuous connections are carriedout many times at the second operation and operations subsequentthereto, data does not change.

Meanwhile, the reason why rounding in even number direction (or roundingin odd number direction) is used in at least one of the orthogonaltransform (Discrete Cosine Transform (DCT)) and the inverse orthogonaltransform (IDCT) as described above in the embodiment of this inventionwill now be described in detail.

Initially, explanation will be given in connection with the reason whyrounding in even number direction or rounding in odd number direction isused without use of rounding in infinity direction as in the previouslydescribed prior art. It is to be noted that while rounding in evennumber direction is mainly described, rounding in odd number directionis also fundamentally the same as the rounding in even number direction,and is shown in FIG. 8D.

Explanation will now be given by using real picture in connection withthe mechanism of accumulation cycle in which rounding errors areaccumulated (accumulation of errors by rounding in infinity direction)by repeating direct digital dubbing.

An actual example 1 in which rounding errors are accumulated by roundingin infinity direction will be described. In this actual example 1,quantization step of DC coefficient is assumed to be qdc=4, andquantization step of AC coefficient is assumed to be qac=2. This is theexample where entire picture samples monotonously increase.

Here, input is assumed to be expressed as follows:

    ______________________________________                                        310     303            303    310                                             310     303            303    310                                             310     303            303    310                                             310     303            303    310                                             ______________________________________                                    

(1-1)

DCT output obtained by allowing this input to undergo Discrete CosineTransform (DCT) is expressed as follows:

    ______________________________________                                        DC      AC1     AC2     AC3       1226 0   14  0                              AC4     AC5     AC6     AC7   =   0    0   0   0                              AC8     AC9     AC10    AC11      0    0   0   0                              AC12    AC13    AC14    AC15      0    0   0   0                              ______________________________________                                    

Thus, DC coefficient of this DCT output becomes equal to 1226. When thisDC coefficient is divided by 4 (re-quantization), 306.5 results.Moreover, with respect to AC coefficients of AC1˜AC15, thosecoefficients are divided by 2 (re-quantization).

Thus, the following expression is obtained.

    ______________________________________                                        306.5    0              7     0                                               0        0              0     0                                               0        0              0     0                                               0        0              0     0                                               ______________________________________                                    

(1-2)

When rounding is implemented thereto, DC coefficient becomes equal to307. Namely,

    ______________________________________                                        307      0              7     0                                               0        0              0     0                                               0        0              0     0                                               0        0              0     0                                               ______________________________________                                    

Inverse-quantization is implemented thereto. With respect to DCcoefficient, this DC coefficient is multiplied by 4, whereby 1228 isobtained. Accordingly, by the quantization/inverse quantization, changeof DC coefficient with respect to the input becomes equal to 2, i.e.,rounding error becomes Erc (=0.5)×4. Namely, change of this DCcoefficient becomes change by processing of coefficient plane. Moreover,with respect to AC coefficients, those AC coefficients are multiplied by2, 14 is obtained. Namely, the following expression is given:

    ______________________________________                                        1228     0              14    0                                               0        0              0     0                                               0        0              0     0                                               0        0              0     0                                               ______________________________________                                    

(1-3)

Here, AC coefficients are assumed to be expressed as follows.

    ______________________________________                                        0        0              14    0                                               0        0              0     0                                               0        0              0     0                                               0        0              0     0                                               ______________________________________                                    

When Inverse Transform (IDCT) is implemented thereto, the followingexpression is obtained.

    ______________________________________                                        3.5     -3.5           -3.5   3.5                                             3.5     -3.5           -3.5   3.5                                             3.5     -3.5           -3.5   3.5                                             3.5     -3.5           -3.5   3.5                                             ______________________________________                                    

(1-4)

Moreover, DC coefficient is assumed to be as follows.

    ______________________________________                                        1228     0              0     0                                               0        0              0     0                                               0        0              0     0                                               0        0              0     0                                               ______________________________________                                    

When Inverse Transform (IDCT) is implemented thereto, the followingexpression is obtained.

    ______________________________________                                        307.0   307.0          307.0  307.0                                           307.0   307.0          307.0  307.0                                           307.0   307.0          307.0  307.0                                           307.0   307.0          307.0  307.0                                           ______________________________________                                    

(1-5)

When the above-mentioned formula (1-3), i.e., IDCT output of ACcoefficient and the above-mentioned formula (1-4), i.e., IDCT output ofDC coefficient are added, the boundary points of the above-mentionedformula (1-3), i.e., IDCT output of AC coefficients are all caused toundergo processing which is positive in polarity. Accordingly, change inthis case is converted into change of DC coefficient.

Change by this rounding processing is expressed as follows:

    ______________________________________                                        0.5      0.5            0.5   0.5                                             0.5      0.5            0.5   0.5                                             0.5      0.5            0.5   0.5                                             0.5      0.5            0.5   0.5                                             ______________________________________                                    

When such change values are caused to undergo DCT, the followingexpression is obtained.

    ______________________________________                                        2        0              0     0                                               0        0              0     0                                               0        0              0     0                                               0        0              0     0                                               ______________________________________                                    

Namely, 2 of DC coefficient becomes change by processing of space plane.

(1-6)

From the above-mentioned formula (1-2), i.e., 2 of DC coefficienttransform value and the above-mentioned formula (1-5), i.e., 2 of DCcoefficient change by DCT after converted into change of DC coefficient,(change by processing of coefficient plane)+(change by processing ofspace plane)=4. This corresponds to one quantization step of DCcoefficient. Accordingly, DC coefficient changes as follows.

    1226→1230

(1-7)

It should be noted that, by converting change of boundary points of ACcoefficients of the above-mentioned formula (1-3) into DC coefficient,this AC coefficient is returned onto the coefficient plane in a mannerto take exactly the same value (=14).

Accordingly, the expression in this case is as follows.

    ______________________________________                                        1230     0              14    0                                               0        0              0     0                                               0        0              0     0                                               0        0              0     0                                               ______________________________________                                    

(1-8)

As stated above, AC coefficient of the above-mentioned formula (1-3)behaves like catalyst so that entirely the same cycle repeats at thesecond operation (second transform/inverse transform processing, firstdubbing processing) and operations subsequent thereto. Accordingly, bythis repetition, all picture samples monotonously increase.

Actual example 2 in which rounding errors are accumulated is taken andexplanation will be given in connection therewith.

In the actual example 2, quantization step of DC coefficient is assumedto be qdc=2 and quantization step of AC coefficient is assumed to beqac=2.

This is the example where 8 samples in total monotonously decrease atthe first row and the fourth row of picture block, and is complicated ascompared to the actual example 1.

Input at this example 2 is assumed to be expressed as follows.

    __________________________________________________________________________    DC   AC1  AC2  AC3     -112 -113 -112 -112                                    AC4  AC5  AC6  AC7  =  -113 -113 -112 -111                                    AC8  AC9  AC10 AC11    -113 -113 -112 -112                                    AC12 AC13 AC14 AC15    -112 -112 -112 -112                                    __________________________________________________________________________

(2-1)

DCT output obtained by allowing this input to undergo DCT is expressedas follows.

    ______________________________________                                        -499.00   -1.3750      0.5000   0.5625                                        -0.1875   -0.3750      0.4375   0.3750                                        0.5000    1.1250       0.0000   0.0625                                        -0.4375   0.3750       -0.1875  0.3750                                        ______________________________________                                    

DC coefficient of this DCT output becomes equal to -499. When thiscoefficient is divided by 2 (re-quantization), -224.5 is obtained.Moreover, also with respect to AC coefficients, those coefficients aredivided by 2 (re-quantization). Thus, the following expression isobtained.

    ______________________________________                                        -224.500  -0.68750     0.25000  0.28125                                       -0.09375  -0.18750     0.28175  0.18750                                       0.25000   0.56250      0.00000  0.03125                                       -0.21875  0.18750      -0.09375 0.18750                                       ______________________________________                                    

(2-2)

When rounding processing is implemented thereto, -225 is obtained withrespect to DC coefficient. Namely, the following expression is obtained.

    ______________________________________                                        -225      -1             0     0                                              0         0              0     0                                              0         1              0     0                                              0         0              0     0                                              ______________________________________                                    

Inverse quantization is implemented thereto. With respect to DCcoefficient, this coefficient is multiplied by 2. Thus, -450 isobtained. Namely,

    ______________________________________                                        -450      -2             0     0                                              0         0              0     0                                              0         2              0     0                                              0         0              0     0                                              ______________________________________                                    

Accordingly, by the quantization/inverse quantization, change of DCcoefficient with respect to the input becomes Erc×2=-1. This change ofDC coefficient becomes change by processing of coefficient plane.

(2-3)

Moreover, after inverse quantization, AC1=-2 and AC9=2 of ACcoefficients are left except for DC coefficient. Here, AC coefficientsare assumed to be expressed as follows

    ______________________________________                                        0       -2              0     0                                               0       0               0     0                                               0       2               0     0                                               0       0               0     0                                               ______________________________________                                    

When Inverse Transform (IDCT) processing is implemented thereto, thefollowing expression is obtained.

    ______________________________________                                        0.000000  0.000000     0.000000 0.000000                                      -1.306563 -0.541196    0.541196 1.306563                                      -1.306563 -0.541196    0.541196 1.306563                                      0.000000  0.000000     0.000000 0.000000                                      ______________________________________                                    

(2-4)

Moreover, DC coefficient is assumed to be expressed as follows.

    ______________________________________                                        -450      0             0     0                                               0         0             0     0                                               0         0             0     0                                               0         0             0     0                                               ______________________________________                                    

When Inverse Transform (IDCT) processing is implemented thereto, thefollowing expression is obtained.

    ______________________________________                                        -112.5   -112.5        -112.5  -112.5                                         -112.5   -112.5        -112.5  -112.5                                         -112.5   -112.5        -112.5  -112.5                                         -112.5   -112.5        -112.5  -112.5                                         ______________________________________                                    

Moreover, the result of Inverse Transform (IDCT) of this DC coefficientcan be expressed as follows.

    __________________________________________________________________________    -112.5  -112.5                                                                             -112.5                                                                             -112.5                                                      -112.5  -112.5                                                                             -112.5                                                                             -112.5  . . . (2-4-1)                                       -112.5  -112.5                                                                             -112.5                                                                             -112.5                                                      -112.5  -112.5                                                                             -112.5                                                                             -112.5                                                         -112.5                                                                             -112.5                                                                             -112.5                                                                             -112.5  0   0   0   0                                       =  -112.0                                                                             -112.0                                                                             -112.0                                                                             -112.0                                                                             +  -0.5                                                                              -0.5                                                                              -0.5                                                                              -0.5                                       -112.0                                                                             -112.0                                                                             -112.0                                                                             -112.0  -0.5                                                                              -0.5                                                                              -0.5                                                                              -0.5                                       -112.5                                                                             -112.5                                                                             -112.5                                                                             -112.5  0   0   0   0                                                                 . . . (2-4-2)                                       __________________________________________________________________________

(2-5)

Here, IDCT output of AC coefficient of the above-mentioned formula (2-3)and IDCT output of DC coefficient of the second term of theabove-mentioned formula (2-4-2), i.e.,

    ______________________________________                                        0       0              0      0                                               -0.5    -0.5           -0.5   -0.5                                            -0.5    -0.5           -0.5   -0.5                                            0       0              0      0                                               ______________________________________                                    

are added. When rounding processing is implemented to added output, thefollowing expression is obtained.

    ______________________________________                                        0        0              0     0                                               -2       -1             0     1                                               -2       -1             0     1                                               0        0              0     0                                               ______________________________________                                    

When the rounded result is transformed, the following expression isobtained.

    ______________________________________                                        -1.000   -2.230         0.000  -0.158                                         0.000    0.000          0.000  0.000                                          1.000    2.230          0.000  0.158                                          0.000    0.000          0.000  0.000                                          ______________________________________                                    

(2-6)

Moreover, change by the processing (rounding of the first term of(2-4-2)) of boundary points of the above-mentioned formula (2-4) isexpressed as follows.

    ______________________________________                                        -0.5    -0.5           -0.5   -0.5                                            0       0              0      0                                               0       0              0      0                                               -0.5    -0.5           -0.5   -0.5                                            ______________________________________                                    

When the above-mentioned expression is transformed, the followingexpression is obtained as follows.

    ______________________________________                                        -1       0              0     0                                               0        0              0     0                                               -1       0              0     0                                               0        0              0     0                                               ______________________________________                                    

(2-7)

From the above-mentioned formulas (2-2) and (2-6), change of DCcoefficient becomes equal to -2 with respect to both the coefficientplane and the space plane, which corresponds to one quantization step.Here, component by processing of space plane newly appears in AC8 of ACcoefficients.

(2-8)

Moreover, in accordance with the result of the above-mentioned formula(2-6), the above-mentioned formula (2-5) is expressed below as theresult of the fact that rounded result is included thereinto.

    ______________________________________                                        -1       -2             0     0                                               0        0              0     0                                               1        2              0     0                                               0        0              0     0                                               ______________________________________                                    

This resultantly serves as catalyst of this cycle.

(2-9)

When the second transform processing is similarly carried out, DC=-451,AC8=-1 are obtained. When these coefficient values are quantized by 2,DC=-225.5 and AC8=-0.5 are obtained.

(2-10)

The quantized coefficient values are rounded so that DC=-226 and AC8=-1are obtained. When inverse quantization is implemented thereto, DC=-452and AC8=-2 are obtained. Changes respectively become Erc×2=-1.

(2-11)

When the portion where components of catalyst overlap with each other issubtracted from the coefficients of DC and AC8, the following expressionis obtained as follows:

    ______________________________________                                        -451        0     0           0   0                                           0           0     0           0   0                                           -3          0     0           0   0                                           0           0     0           0   0                                           ______________________________________                                    

When this expression is inverse-transformed, the following expression isobtained.

    ______________________________________                                        -113.5   -113.5        -113.5  -113.5                                         -112.0   -112.0        -112.0  -112.0                                         -112.0   -112.0        -112.0  -112.0                                         -113.5   -113.5        -113.5  -113.5                                         ______________________________________                                    

Values of transform processing by processing of the boundary point areas indicated by the above-mentioned formula (2-6).

(2-12)

From the results of the above-mentioned formula (2-10) and theabove-mentioned formula (2-11), DC and AC8 are both -2 with respect toboth coefficient plane and space plane, which correspond to change ofone quantization step.

(2-13)

Components of catalyst do not change even if transform/inverse transformprocessing are repeated. At times subsequent thereto, cycle of theabove-mentioned formulas (2-8)˜(2-13) are repeated.

The condition of accumulation cycle where rounding errors areaccumulated as in the above-described actual example will now bedescribed.

Initially, let consider the condition of accumulation cycle. Asindicated in the above-described actual example, relation ofcoefficients relating to the accumulation cycle is very complicated.Here, in order to closely examine picture emphasis pattern, variousconditions are determined. This also corresponds to explanation of wayof thinking of measure with respect to accumulation of rounding errorsin the embodiment of this invention (i.e., the reason why rounding ineven number direction is used).

First, since transform and inverse transform (DCT-IDCT) processing havesufficient operation accuracy, there is no accumulation of errors exceptfor boundary points in rounding. Accordingly, only boundary point inrounding participates in the accumulation cycle.

Secondly, change by processing of boundary point of space plane is addedto change by processing of boundary point of coefficient plane, therebyrecursively bringing about shift of one quantization step on thecoefficient plane. When any component except for boundary point of spaceplane is included in change of the former processing, increment ofboundary point by rounding of the space plane is not returned (exertedon) to the boundary point of coefficient plane for a second time fromsymmetry of DCT-IDCT. As a result, accumulation cycle is cut off.Accordingly, accumulation cycle takes place only when boundary point ofspace plane exists on the coefficient plane and boundary point ofcoefficient plane exists on the space plane.

Thirdly, when, e.g., quantization step size qxx is 3, distribution oferrors falls within the digit oriented error range as shown in FIG. 3.

For example, if the range of error of qxx=4 is -Δ/2˜Δ/2, when qxx=3 inthe FIG. 3 mentioned above, the range of error is expressed as follows:

    (-3/4)×(Δ/2)˜(3/4)×(Δ/2)

If the range of error of qxx=2 is -Δ'/2˜Δ'/2, the above-mentioned rangeof error is expressed as follows:

    (-3/2)×(Δ'/2)×(3/2)×(Δ'/2)

Fourthly, when consideration is made in connection with the range on thespace plane within which change by boundary point processing ofcoefficient plane should fall in order to cause accumulation cycle,e.g., the influence of error 0.5 of boundary point of coefficient planehas been assumed to be 2.5 on the space plane. On the space plane, sucherror value is rounded into 3.0. Error by rounding at this time is 0.5.Since DCT/IDCT are symmetrical and reversible, error value becomesE=0.5/5=0.1 on the next coefficient plane. As a result, accumulationcycle of the boundary point is cut off.

On the other hand, when there results boundary point of space planewithout taking a transfer form, E=0.5 is provided by similarcalculation. As a result, accumulation cycle is not cut off.

    ______________________________________                                                Coefficient                                                                           →                                                                            Space     →                                                                          Coefficient                                       Plane         Plane         Plane                                     ______________________________________                                        Transfer  Erc = 0.5   (ex)2.5→3.0                                                                        Ers = 0.5                                                                     E = 0.1                                     Non-transfer                                                                            Erc = 0.5   (ex)0.5→1.0                                                                        Ers = 0.5                                                                     E = 0.5                                     ______________________________________                                    

Accordingly, it is seen that only when the influence by error ofcoefficient plane falls within one quantization step on the space plane,accumulation cycle takes place. When qdc≠qac, greater quantization isquantization at that time.

Results obtained with real pictures shown in the above-described actualexample are in conformity with the above.

From facts as described above, space plane output is shifted to one sidein polarity by DC coefficient. As a result, processing of boundary pointby rounding of the space plane is converted into processing of one sidein polarity, thereby shifting mean value of errors. This is the greatfactor to cause monotonous increase (decrease).

As described above, the accumulation cycle takes place when processingis rounding which is integer operation (non-linear processing), and isvery special case where respective coefficients of coefficient plane andspace plane samples are satisfactorily related to each other. This isthe case which is low from a viewpoint of probability. As the fact thatthis is low probability case is supported, it cannot be said that suchphenomenon takes place at all times even with respect to any pattern,and picture emphasis patters confirmed by real picture are patterns inthe first, second and third conditions described in the condition of theaccumulation cycle.

The cause in which the accumulation cycle takes place resides inemployment of method of balancing the distribution of errors by polarityof positive and negative (i.e., rounding in infinity direction). In thebit rate reduction system utilizing transform encoding, there is noclose correspondence relationship except for DC coefficient betweenpolarity of the coefficient plane and polarity of the space plane. Thereare instances where the influence of processing of boundary point bycombination of coefficients is converted into processing one side inpolarity at all times on the space plane. As a result, distribution oferrors does not incline in a balance direction thereof, but deviates inone direction. Errors resulting therefrom are accumulated.

In this way, cycle of monotonous increase/decrease of specific picturepattern is constructed by the accumulation cycle, thus failing torealize complete re-construction irrespective of operation accuracy oftransform processing.

Further, since picture pattern emphasized by monotonous increase ordecrease becomes geometric pattern, picture quality of multi-generationis greatly injured.

From facts as described above, in this embodiment, a method of balancingdistribution of errors irrespective of polarity on the space plane isemployed.

Namely, in this embodiment, a method of balancing distribution of errorswith even number value being as reference for rounding of output ofspace plane, i.e., rounding in even number direction is employed. Itshould be noted that, as a method of balancing distribution of errorsirrespective of polarity on the space plane, a method of balancingdistribution of errors with odd number being as reference for roundingof output of space plane, i.e., rounding in odd number direction may beemployed.

By such measure, complete re-construction of digital direct dubbing isrealized.

FIG. 10 shows the state of degradation of S/N of Y signal and PR/PBsignal of video signal in the case where dubbing is straight repeated(simulation result after a plurality of dubbing operations) whenoperation accuracy of DCT is 12 bits, 13 bits and 14 bits. Evaluationpicture has compression rate of 1/2. In this simulation, operations ofDCT, IDCT are carried out by floating-point, and rounding into integeruses function based on IEEE 754 standard, but rounding is carried out bymethod of simple rounding (rounding in positive direction) inquantization.

Moreover, simulation result in the case where rounding in infinitydirection is used is shown in FIG. 11, and simulation result in the casewhere rounding in even number direction is used in this embodiment isshown in FIG. 12.

In the case of rounding in infinity direction shown in FIG. 11, curve ofS/N deterioration becomes gentle although degree of gentleness is slightas compared to the case of rounding in positive direction shown in FIG.10.

On the contrary, in rounding in even number direction employed in thisembodiment shown in FIG. 12, degradation of S/N becomes gentle ascompared to the rounding in positive direction or the rounding ininfinity direction, and data is converged at early generation. It isseen that greater effect is provided particularly in the case of 12 bitsin which operation accuracy of DCT is low as shown in FIG. 13.Additionally, simulation results of rounding in infinity direction androunding in positive direction are shown together in FIG. 13.

Moreover, while DCT is used in the above-described embodiment, bitreduction by so called Wavelet transform is more excellent in picturequality as compared to DCT. Since particularly Wavelet transform by socalled Harr base can be realized by addition and subtraction ofintegers, and is permitted to undergo frequency decomposition afterblock division is carried out in the same manner as DCT, hardware scalecan be also reduced.

In view of this, the portion of DCT in the above-described embodiment isreplaced by 10 division Discrete Wavelet Transform (DWT) of 8×8 by theHart base, thus to carry out simulation. It should be noted thatoperation accuracy of DWT is 14 bits at maximum unlike DCT, and norounding error takes place in this case. Since the same rounding systemas that of quantization is employed in DWT, IDWT, there are threerounding portions. These rounding operations are compared in connectionwith the rounding in positive direction, the rounding in infinitydirection and the rounding in even number direction.

The results are as shown in FIGS. 14˜17. It is to be noted thatevaluation picture and compression ratio are the same as those of theabove-described DCT. Moreover, in FIGS. 14˜17, there is shown simulationresult in the case where Y, PB, PR signals of video signal are used anddubbing is straight repeated when operation accuracy of DWT is 12 bits,13 bits and 14 bits. The case using rounding in positive direction isshown in FIG. 14, the case where rounding in infinity direction is usedis shown in FIG. 15, and the case where rounding in even numberdirection is used. In FIG. 17, there is shown simulation results ofrounding in even number direction, rounding in infinity direction androunding in positive direction in the case of 12 bits in which operationaccuracy of DWT is low.

From these FIGS. 14˜17, it is seen that the rounding in positivedirection and the rounding in infinity direction show the same tendency,degradation of S/N is great at DWT operation accuracy 12 bits, andoperation errors are accumulated to more degree according as andgenerations overlap with each other.

On the contrary, in the rounding in even number direction, deteriorationof S/N is small even at 12 bits, and data is converged at thethird˜fourth generations.

From pacts as described above, it is seen that even in the case whereoperation accuracy is insufficient, as compared to conventional rounding(rounding in positive direction or rounding in infinity direction), evennumber rounding (odd number rounding) has less accumulation of errors.This is because since according as bits to be rounded off become lesser,the probability that 0.5 takes place becomes higher, the effect ofrounding in even number direction is exhibited to more degree.

In VTR for carrying out bit rate reduction where high picture quality isrequired, it is desirable to ensure sufficient operation accuracy and tocarry out rounding in even number direction. Also in the case wheretransform/inverse transform are repeated as in the matrixtransformation, the rounding in even number direction is effective forreducing accumulated error quantity.

As described above, in the embodiment of this invention, rounding ineven number direction (or rounding in odd number direction) is used intransform encoding sufficiently having operation accuracy, therebymaking it possible to prevent accumulation of the influence byprocessing of boundary points which is singular points in rounding.Thus, monotonous increase/decrease of amplitude of fixed picture patterncan be prevented. By this effect, it is possible to realize transformsystem in which even if complete re-construction, i.e., multi-generationis carried out many times, there is no picture deterioration. In otherwords, in continuous connection of plural times of efficientencoding/decoding apparatuses, picture deterioration is held down tominimum level so that data can be converged into fixed value.

It is to be noted since this invention is common not only to digitalVTR, but also to system employing bit reduction by transform encoding,this invention can be also applied to other similar systems, e.g., audiosystem, etc.

Finally, patterns where picture is emphasized in accumulation cycle(picture emphasis patterns) are taken as an example.

It is considered that variations of patterns in the case where thecondition of boundary point of coefficient plane is inputted to inversetransform matrix, so accumulation cycle takes are as indicated by group(1) shown in FIG. 18˜group (4) shown in FIG. 21.

In this case, in the groups of (1)˜(4), re-quantization step and inputcoefficient values are assumed to be as follows:

    ______________________________________                                        Re-quantization step                                                                        Input coefficient value                                         ______________________________________                                        (1) qdc = qac = 1                                                                           DC = -1˜+1, ACx = -1˜+1                             (2) qdc = qac = 2                                                                           DC = -1˜+1, ACx = -1˜+1                             (3) qdc = 4   DC = -2˜+2                                                (4) qdc = 2, qac = 1                                                                        DC = -2˜+2, ACx = -1˜+1                             ______________________________________                                    

Moreover, input coefficient value format is assumed to be as follows.

    ______________________________________                                        DC,         AC1,       AC2,       AC3,                                        AC4,        AC5,       AC6,       AC7,                                        AC8,        AC9,       AC10,      AC11,                                       AC12,       AC13,      AC14,      AC15                                        ______________________________________                                    

The accumulation cycle is the special case where rounding which isinteger operation (non-linear processing), and respective coefficientsof coefficient plane and space plane samples are satisfactorily relatedto each other. For example, patterns of groups of (1), (2), (3) shown inFIGS. 18˜21 can be enumerated.

What is claimed is:
 1. An efficient encoding/decoding apparatuscomprising:orthogonal transform means for orthogonally transforming adigital signal obtained by allowing an analog signal to undergoanalog/digital conversion; and inverse orthogonal transform means forinverse-orthogonally transforming the orthogonally transformed digitalsignal, wherein rounding of endpoints of segments in even numberdirection or in odd number direction is used in at least one of theorthogonal transform processing and the inverse orthogonal transformprocessing.
 2. An efficient encoding/decoding apparatus as set forth inclaim 1,wherein there are provided: quantizing means for quantizing thedigital signal which has undergone the orthogonal transform processing;and inverse quantizing means for inverse-quantizing a digital signalwhich is not yet caused to undergo the inverse orthogonal transformprocessing.
 3. An efficient encoding/decoding apparatus as set forth inclaim 1,wherein the orthogonal transform processing is Discrete CosineTransform processing, and the inverse orthogonal transform processing isInverse Discrete Cosine Transform processing.
 4. An efficientencoding/decoding apparatus as set forth in claim 1,wherein theorthogonal transform processing is Discrete Wavelet Transform (DWT)processing, and the inverse orthogonal transform processing is InverseDiscrete Wavelet Transform (IDWT) processing.
 5. The efficientencoding/decoding apparatus of claim 1, wherein the endpoints of realnumber segments having lengths of Δ and centered about 0, ±Δ, ±2Δ, ±3Δ .. . ±nΔ are rounded to a nearest one of said even number and odd number.